Tools › Structures › Beams › Lateral-Torsional Buckling

Lateral-Torsional Buckling of Beams

Lateral-torsional buckling strength of a doubly symmetric I-beam or a channel bent about its strong axis: the elastic critical moment of Timoshenko (warping and Saint-Venant torsion), the AISC 360 limiting lengths Lp and Lr, the nominal flexural strength Mn in the plastic, inelastic and elastic ranges with the moment-gradient factor Cb, and a margin of safety against the applied moment. The section comes from plate dimensions (area, moments of inertia, plastic modulus, torsion constant and warping constant computed exactly from the drawn outline), from a saved section, or from properties typed in; a saved MIL-HDBK-5J material fills E, G and Fy.

  • Elastic critical moment Mcr = Cb (π/Lb) √(E Iy G J + π² E² Iy Cw / Lb²)

  • AISC 360-16 Section F2: Lp, Lr, Fcr and Mn with the moment-gradient factor Cb (entered or from the quarter-point moments)

  • Section from plate dimensions, from a saved section (shear centre and Cw from the Section Properties tool) or from typed properties

  • Chart of Mn against the unbraced length with the applied moment marked

Beam, Section and Loading

Unit System: /

Section Source

Plate Dimensions (doubly symmetric I)





Section Properties (typed or loaded)

Sign in










Material

Sign in




Unbraced Length and Moment Gradient






Applied Moment






References

American Institute of Steel Construction (2016). Specification for Structural Steel Buildings. ANSI/AISC 360-16, Chicago, IL.

Timoshenko, S. P., and Gere, J. M. (1961). Theory of Elastic Stability, 2nd ed. McGraw-Hill, New York.

Ziemian, R. D. (ed.) (2010). Guide to Stability Design Criteria for Metal Structures, 6th ed. John Wiley and Sons, Hoboken, NJ.

Galambos, T. V., and Surovek, A. E. (2008). Structural Stability of Steel: Concepts and Applications for Structural Engineers. John Wiley and Sons, Hoboken, NJ.

Trefftz, E. (1935). "Über den Schubmittelpunkt in einem durch eine Einzellast gebogenen Balken." Zeitschrift für angewandte Mathematik und Mechanik, Vol. 15, No. 4, pp. 220–225.

Worked Examples

Published examples this tool reproduces; each page lists the inputs to enter and the printed answers.

All worked examples

DISCLAIMER: The methods and calculation on aNOWysis.com are provided as means to educate the reader. There is no warranty, expessed or implied, as to the relevance or accuracy of the methods or calculations. All calculations should be checked by a qualified analyst for appropriateness and accuracy. We will not be held liable for any damages, injuries or deaths caused by using methods or calculations from this site.